Solve for $x$ and $y$ using elimination. ${-6x-3y = -66}$ ${-5x+6y = -4}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ ${-12x-6y = -132}$ $-5x+6y = -4$ Add the top and bottom equations together. $-17x = -136$ $\dfrac{-17x}{{-17}} = \dfrac{-136}{{-17}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-6x-3y = -66}\thinspace$ to find $y$ ${-6}{(8)}{ - 3y = -66}$ $-48-3y = -66$ $-48{+48} - 3y = -66{+48}$ $-3y = -18$ $\dfrac{-3y}{{-3}} = \dfrac{-18}{{-3}}$ ${y = 6}$ You can also plug ${x = 8}$ into $\thinspace {-5x+6y = -4}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ + 6y = -4}$ ${y = 6}$